We present an efficient, accurate approach for solving flow problems in heterogeneous porous formations. We do so by obtaining higher-order solutions of the prediction and the associated uncertainty of reservoir flow quantities using the moment-equation approach based on Karhunen-Loéve decomposition (KLME). The KLME approach is developed on the basis of the Karhunen-Loéve (KL) decomposition, polynomial expansion, and perturbation methods. We conduct Monte Carlo simulations (MCS) and compare MCS results against different orders of approximations from the KLME method for some two- and three-dimensional computational examples. These examples demonstrate that this KLME method is computationally more efficient than both Monte Carlo simulations and the conventional moment-equation method. The KLME approach allows us to evaluate higher-order terms that are needed for the highly heterogeneous reservoirs. In addition, just like the Monte Carlo method the KLME approach can be implemented with existing simulators in a straightforward manner and are inherently parallel. The efficiency of the KLME method makes it possible to simulate fluid flow in large-scale heterogeneous formations.